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Recent problems solved by 'stanbon'
stanbon answered: 57222 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>NextEquations/369255: Hi, I have to find the vertical and horizontal asymptotes, as well as the y-intercept for the following:
If I'm not mistaken,
vertical asymptote = 
horizontal asymptotes are and 
I calculated the y-intercept by plugging 0 in for x and got 1/2, but when I graph the equation it doesn't look like 1/2. I appreciate any help you can provide :)
1 solutions
Answer 263116 by stanbon(57290)   on 2010-11-10 19:37:16 (Show Source):
You can put this solution on YOUR website!find the vertical and horizontal asymptotes, as well as the y-intercept for the following:
y=(1 + 2x)/(x+2)
If I'm not mistaken,
vertical asymptote =
horizontal asymptote: y = 2x/x = 2
--------------------------------------------
I calculated the y-intercept by plugging 0 in for x and got 1/2, but when I graph the equation it doesn't look like 1/2.
---
x-int: Solve [(1+2x)/(x+2)] = 0
True when 1+2x = 0
2x = -1
x = -1/2
=========================
===================================================
Cheers,
Stan H.
========
|
Mixture_Word_Problems/369251: Nick has two cans of white paint, one with a 2% yellow pigment and the other with a 5% yellow pigment. He wants to mix the two paints to get paint with a 4% yellow pigment. How much of the 5% yellow pigment paint should be mixed with 0.4 gallon of the 2% yellow pigment paint to get the desired paint?
1 solutions
Answer 263113 by stanbon(57290) on 2010-11-10 19:30:39 (Show Source):
You can put this solution on YOUR website!Nick has two cans of white paint, one with a 2% yellow pigment and the other with a 5% yellow pigment. He wants to mix the two paints to get paint with a 4% yellow pigment. How much of the 5% yellow pigment paint should be mixed with 0.4 gallon of the 2% yellow pigment paint to get the desired paint?
-----------------
Equation:
yellow + yellow = yellow
0.05x + 0.02*0.4 = 0.04(x+0.4)
----
Multiply thru by 100 to get:
5x + 2*0.4 = 4x+4*0.4
x = 2*0.4
x = 0.8 gallons (amt. of 5% paint needed in the mixture)
===================================
Cheers,
Stan H.
|
Mixture_Word_Problems/369250: According to Wikipedia, the best-selling album in 2005 was Mariah Carey’s The Emancipation of Mimi. The best-selling album in 2004 was the album Confession by Usher. Confession sold 0.94 million copies less than twice the amount The Emancipation of Mimi sold. The sum of these two albums was 13.97 million copies. Determine the sales of both albums
1 solutions
Answer 263106 by stanbon(57290) on 2010-11-10 19:24:38 (Show Source):
You can put this solution on YOUR website!The best-selling album in 2004 was the album Confession by Usher.
Confession sold 0.94 million copies less than twice the amount The Emancipation of Mimi sold.
The sum of these two albums was 13.97 million copies.
Determine the sales of both albums.
-----
Equations:
c + e = 13.97 million
c = 2e-0.94
----
Substitute for "c" and solve for "e":
2e-0.94 + e = 13.97
3e = 14.91
e = 4.97 million (# of "Emancipation" sold)
---
Since c = 2e-0.94 = 9 million (# of "Confession" sold)
=======================================================
Cheers,
Stan H.
|
Quadratic_Equations/369244: Graph the quadratic function f(x)=7(x+1)^2+4: state the ordeed pairs representing the x-intercept and y-intercept (if any) and the vertex or the parabola.
1 solutions
Answer 263104 by stanbon(57290) on 2010-11-10 19:17:20 (Show Source):
You can put this solution on YOUR website!Graph the quadratic function f(x)=7(x+1)^2+4:
state the ordeed pairs representing the x-intercept and y-intercept (if any) and the vertex or the parabola.
----
Vertex: (-1,4)
y-int: (0,11)
x-int: none
-------
=====
Cheers,
Stan H.
|
Linear_Algebra/368956: (x + 6) divided by the fraction x^2 + 5x - 6 / x^2 + 7x - 8 please find the quotient
1 solutions
Answer 262903 by stanbon(57290) on 2010-11-10 08:18:19 (Show Source):
You can put this solution on YOUR website!(x + 6) divided by the fraction x^2 + 5x - 6 / x^2 + 7x - 8
please find the quotient
-----------------------
(x+6)/[(x+6)(x-1)/(x+8)(x-1)]
----
Invert the denominator and multiply:
----
(x+6)
----
Cancel the (x+6) and (x-1) factors to get:
----
= (x+8)/(x+6)
=================
Cheers,
Stan H.
|
Trigonometry-basics/368957: Ok I'm having trouble proving these harder identities.
The homework says prove that each of the following identities is true
(2sec^2)x-(2sec^2)x(sin^2)x-(sin^2)x-(cos^2)x=1
It's w/o the parenthesis in the homework, I just didn't know how to seperate the squares for the x's.
I tried multiplying by (2cos^2)x to get rid of the sec's but I'm getting nowhere with it. Here's what I did even though I know it's wrong:
*-1 then (2cos^2)x
=-(2cos^4)x+(4cos^2)x(sin^2)x=0
/(2cos^2)x
=(-cos^2)x+(2cos^2)x(sin^2)x=0
Then I don't see anywhere to go!
1 solutions
Answer 262900 by stanbon(57290) on 2010-11-10 08:13:04 (Show Source):
You can put this solution on YOUR website!(2sec^2)x-(2sec^2)x(sin^2)x-(sin^2)x-(cos^2)x=1
-------------------------------------------------
2sec^2 - 2sec^2*sin^2 -[sin^2+cos^2] = 1
----
2sec^2[1-sin^2] - 1 = 1
----
2sec^2[cos^2] = 2
---
2(1) = 2
2 = 2
==========
Cheers,
Stan H.
|
Linear-systems/368958: Find the consecutive even numbers whose sum is 108.
1 solutions
Answer 262897 by stanbon(57290) on 2010-11-10 08:08:55 (Show Source):
You can put this solution on YOUR website!Find the consecutive even numbers whose sum is 108.
-----
1st: 2x
2nd: 2x+2
-----
Equation:
2x + 2x+2 = 108
4x = 106
x = 26.5
----
1st: 2x = 53
2nd: 2x+2 = 55
-----
There are no two consecutive EVEN numbers whose sum is 108.
=============
Cheers,
Stan H.
|
Expressions-with-variables/368955: 1. a electrician requires 65 min to install a ceiling fan. The electrican and an apprentice working together take 40 min to install the fan. How long would it take the apprentice working alone to install the ceiling fan?
2. 3 - x2 + x . 2x2 + x - 3
________ ___________ ____________
x-2 2x3+3x2 x2 + 3x +2
1 solutions
Answer 262891 by stanbon(57290) on 2010-11-10 08:05:07 (Show Source):
You can put this solution on YOUR website!an electrician requires 65 min to install a ceiling fan. The electrican and an apprentice working together take 40 min to install the fan. How long would it take the apprentice working alone to install the ceiling fan?
----
Electrician rate: 1/65 job/min
Together rate:::: 1/40 job/min
Aprentice rate::: 1/x job/min
-----------------------------------
Equation:
rate + rate = together rate
1/65 + 1/x = 1/40
Multiply thru by 40*65x to get:
---
40x + 40*65 = 65x
25x = 40*65
25x = 2600
x = 2600/25
x = 104 minutes (time the apprentice would need)
==================
Cheers,
Stan H.
|
Linear-systems/368947: eight years ago, the sum of Peter's age and Carlo's age is at least 26. Peter is 4 years older than Carlo. At least how old is Carlo now ?
1 solutions
Answer 262889 by stanbon(57290) on 2010-11-10 08:00:48 (Show Source):
You can put this solution on YOUR website!Eight years ago, the sum of Peter's age and Carlo's age is at least 26.
Peter is 4 years older than Carlo. At least how old is Carlo now ?
----------------
Equations:
(P-8+C-8)>=26
P = C+4
-----
Substitute and solve for "C":
(C+4+C-16) >= 26
2C-12 >= 26
2C >=38
C >= 19 (Carlo's age now)
===================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/368857: Alex stocks up for winter He buys 36 cans of vegetables he payes 80 cents per can for tomatoes and 40 cents per can for corn for a total cost of 20.80.
how many cans of corn does he buy?
1 solutions
Answer 262794 by stanbon(57290) on 2010-11-09 22:00:10 (Show Source):
You can put this solution on YOUR website! Alex stocks up for winter.
He buys 36 cans of vegetables he payes 80 cents per can for tomatoes and 40 cents per can for corn for a total cost of 20.80.
how many cans of corn does he buy?
-----
Quantity Eq:: t + c = 36
Value Eq::: 80t +40c = 2080 cents
------------------------------------------
Multiply thru by 80 to get:
80t + 80c = 80*36
---
Subtract that from the Value Eq and solve for "c":
-40c = -800
c = 20 (# of can of corn bought)
=====================================
Cheers,
Stan H.
==============
|
logarithm/368856: what is the solution for log of x-7 base 5= -2 solving for x?
1 solutions
Answer 262785 by stanbon(57290) on 2010-11-09 21:49:19 (Show Source):
You can put this solution on YOUR website!what is the solution for log of x-7 base 5= -2 solving for x?
-------------
log5(x-7) = -2
----
(x-7) = 5^(-2)
------
x-7 = 1/25
---
x = 7 1/25
=====================
Cheers,
Stan H.
|
Rate-of-work-word-problems/368805: I need help solving this problem.
There is a table given that says weight in pounds, x: 5,10,15
then cost to mail, y: $7, $11, $15
then it asks..
How much does it cost per pound to mail a package?
Then.. What would a 16 pound package cost to mail?
Thanks for the help!
1 solutions
Answer 262750 by stanbon(57290) on 2010-11-09 21:16:01 (Show Source):
You can put this solution on YOUR website!There is a table given that says
weight in pounds, x: 5, 10, 15
then cost to mail, y: $7, $11, $15
then it asks..
How much does it cost per pound to mail a package?
Then.. ----
slope = (11-7)/(10-5) = 4/5 = 80 cents per pound
-----
Equation:
y = mx+b
7 = (4/5)5 + b
b = 3
---
Equation:
c(x) = (4/5)x + 3
What would a 16 pound package cost to mail?
c(16) = (4/5)*16 + 3
c(16) = 64/5+3 = $15.80
==========================
Cheers,
Stan H.
==========================
|
Equations/368806: john has 3 pairs of pants, 4 shirts and 2 belts. how many combinations can he wear? can you tell me a formula for this, i can do it manually but would like a formula, thx mike
1 solutions
Answer 262742 by stanbon(57290) on 2010-11-09 21:06:59 (Show Source):
You can put this solution on YOUR website!john has 3 pairs of pants, 4 shirts and 2 belts. how many combinations can he wear? can you tell me a formula for this, i can do it manually but would like a formula,
-----
Counting Principle:
If step one of a process can be done in n1 ways
and step k can be done in nk ways,
the process can be done in n1*n2*n3*...*nk ways
-------------------------------------
Your problem
# of combinations is 3*4*2 = 24 ways
=======================================
Cheers,
Stan H.
|
test/368803: Multiply and simplify
(9a^2)/(5a^2-30a+45)*(5a-15)/(3a)
1 solutions
Answer 262734 by stanbon(57290) on 2010-11-09 20:54:36 (Show Source):
You can put this solution on YOUR website! Multiply and simplify
(9a^2)/(5a^2-30a+45)*(5a-15)/(3a)
-------
(9a^2)/(5(a^2-6a+9)*(5(a-3))/(3a)
---
Cancel factors common to a numerator and a denominator,
such as 3a,5,(a-3), to get:
------
= (3a)/(a-3)
------
Cheers,
Stan H.
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test/368802: factor completely
150r^2+360rg+216g^2
1 solutions
Answer 262728 by stanbon(57290) on 2010-11-09 20:49:20 (Show Source):
You can put this solution on YOUR website!factor completely
150r^2+360rg+216g^2
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= 2[75r^2 + 180rg + 108q^2]
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= 2*3[25r^2 + 60rg + 36]
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= 6(5r+6)(5r+6)
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Cheers,
Stan H.
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Probability-and-statistics/368750: In the department of education at UR university, student records suggest that the population of students spends an average of 5.5 hrs per week playing organized sports. The population's standard deviation is 2.2 hrs per week. Based on a sample of 121 students, healthy lifestyles Inc. (HLI) would like to apply the central limit theorem to make various estimates.
Compute the standard error of the sample mean
what is the chance HLI will find a sample mean between 5 and 6 hrs?
calculate the probability that the sample mean will be between 5.3 and 5.7 hrs
how strange would it be to obtain a sample mean greater than 6.5 hrs?
1 solutions
Answer 262708 by stanbon(57290) on 2010-11-09 20:13:48 (Show Source):
You can put this solution on YOUR website!In the department of education at UR university, student records suggest that the population of students spends an average of 5.5 hrs per week playing organized sports. The population's standard deviation is 2.2 hrs per week.
-----------------------
Based on a sample of 121 students, healthy lifestyles Inc.
(HLI) would like to apply the central limit theorem to make various estimates.
-----------------------
Compute the standard error of the sample mean?
Ans: 2.2/sqrt(121) = 0.2
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What is the chance HLI will find a sample mean between 5 and 6 hrs?
t(5) = (5-5.5)/0.2 = -2.5
t(6) = (6-5.5)/0.2 = +2.5
P(5< x-bar <6) = P(-2.5< t < 2.5 when df=120) = 0.9862
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Calculate the probability that the sample mean will be between 5.3 and 5.7 hrs
how strange would it be to obtain a sample mean greater than 6.5 hrs?
---
Find the t-values; then find the probabilities.
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Cheers,
Stan H.
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Exponential-and-logarithmic-functions/368745: Does following represent a function? Explain.
X's: 3,4,5,-1,-2,-2
Y's: 5,9,12,3,0,-4
1 solutions
Answer 262704 by stanbon(57290) on 2010-11-09 20:00:45 (Show Source):
You can put this solution on YOUR website! Does following represent a function? Explain.
X's: 3,4,5,-1,-2,-2
Y's: 5,9,12,3,0,-4
----
Not a function, because -2 is associated with 0
and -2 is associated with -4.
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Cheers,
Stan H.
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Coordinate-system/368742: How do I find the range of a function with a given domain such as x is less than or equal to 0?
1 solutions
Answer 262700 by stanbon(57290) on 2010-11-09 19:55:32 (Show Source):
You can put this solution on YOUR website!How do I find the range of a function with a given domain such as x is less than or equal to 0?
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That depends on the equation (rule) that defines the function.
Cheers,
Stan H.
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Probability-and-statistics/368708: A bag contains green and yellow color tiles. You pick two tiles at random with out replacing the first one. The probability that the first tile is yellow is 3 to 5. The probability of drawing two yellow tiles is 12 to 35. Find the probability that the second tile you pick is yellow.
1 solutions
Answer 262694 by stanbon(57290) on 2010-11-09 19:24:22 (Show Source):
You can put this solution on YOUR website! A bag contains green and yellow color tiles. You pick two tiles at random with out replacing the first one.
The probability that the first tile is yellow is 3/5.
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The probability of drawing two yellow tiles is 12 to 35.
P(yellow and yellow) = P(y)*P(y|y)
12/35 = (3/5)*P(y|y)
P(y|y) = 12/21 = 4/7
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Find the probability that the second tile you pick is yellow.
P(y|y) = 4/7
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Cheers,
Stan H.
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Quadratic_Equations/368684: Car speed. On a sales trip, Mark drives the 600 mi to Richmond averaging a certain speed. The return trip is made at an average speed that is 10 mph slower. Total time for the round trip is 22 hr. Find Mark’s average speed on each part of the trip.
1 solutions
Answer 262691 by stanbon(57290) on 2010-11-09 19:13:03 (Show Source):
You can put this solution on YOUR website! Car speed. On a sales trip, Mark drives the 600 mi to Richmond averaging a certain speed. The return trip is made at an average speed that is 10 mph slower. Total time for the round trip is 22 hr. Find Mark’s average speed on each part of the trip.
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To Richmond DATA:
distance = 600 miles ; rate = x mph ; time = 600/x hrs
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From Richmond DATA:
distance = 600 miles ; rate = x-10 mph ; time = 600/(x-10) hrs.
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Equation:
time + time = 22 hrs
600/x + 600/(x-10) = 22
----
600(x-10) + 600x = 22x(x-10)
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1200x - 6000 = 22x^2-220x
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22x^2 - 1420x + 6000 = 0
11x^2 - 710x + 3000 = 0
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Positive solution:
x = 60 mph (rate to Richmond)
x-10 = 50 mph (rate from Richmond)
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Cheers,
Stan H.
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Word_Problems_With_Coins/368659: Sam has $2.05 in quarters and dimes. He has 4 more quarters than dimes. Find the number he has of each coin
1 solutions
Answer 262681 by stanbon(57290) on 2010-11-09 18:26:57 (Show Source):
You can put this solution on YOUR website!Sam has $2.05 in quarters and dimes. He has 4 more quarters than dimes. Find the number he has of each coin
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Quantity Eq:: q = d + 4
Value Eq:::: 25q+10d = 205
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Substitute for "q" and solve for "d":
25(d+4) + 10d = 205
35d = 105
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d = 3 (# of dimes)
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Since q = d+4, q = 7 (# of quarters)
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Cheers,
Stan H.
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Age_Word_Problems/368622: Louise is 26 years older than her daughter. Louise's age is two more than four times her daughter's age. How old is her daughter?"
1 solutions
Answer 262679 by stanbon(57290) on 2010-11-09 18:19:37 (Show Source):
You can put this solution on YOUR website!Louise is 26 years older than her daughter. Louise's age is two more than four times her daughter's age. How old is her daughter?"
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Equation:
L = d + 26
L = 4d + 2
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Substitute and solve for "d":
d+26 = 4d+2
3d = 24
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d = 8 yrs. old (daughter's age now)
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Cheers,
Stan H.
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Quadratic_Equations/368621: Hello. Can you please help me? It's greatly appreciated.
solve equation by factoring:
3x^2 - 13x -10 thank you!
1 solutions
Answer 262660 by stanbon(57290) on 2010-11-09 17:18:59 (Show Source):
You can put this solution on YOUR website!solve equation by factoring:
3x^2 - 13x -10
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You cannot "solve" the expression unless it is an equation.
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Assume 3x^2 - 13x - 10 = 0
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3x^2 -15x+2x -10 = 0
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3x(x-5)+2(x-5) = 0
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(x-5)(3x+2) = 0
x = 5 or x = -3/2
===========================
Cheers,
Stan H.
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Sequences-and-series/368338: This is a 5th grade math problem that I heard from a friend and I am curious to learn the answer.
A student has a test with 2 parts. Part A questions are worth 2 points and Part B are worth 5 points each. The student gets all the questions right in part A but misses 1 question in part B. The student scores an 85% on the overall test. How many questions are on the test? Help I tried to do:
2x__ +5x___ (-5) = .85 but I can't make it come out to 85%
Thanks for your help
1 solutions
Answer 262501 by stanbon(57290) on 2010-11-09 09:52:33 (Show Source):
You can put this solution on YOUR website!A student has a test with 2 parts.
Part A questions are worth 2 points and Part B are worth 5 points each.
The student gets all the questions right in part A but misses 1 question in part B.
-------------------------
The student scores an 85% on the overall test. How many questions are on the test? Help I tried to do:
2x__ +5x___ (-5) = .85 but I can't make it come out to 85%
===========================================================
1st part:
x questions
2x points
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2nd part:
y questions
5(y-1)
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Average = (total points)/(# of questions)
[(2x)+5y-5]/(x+y) = 0.85
2x + 5y - 5 = 0.85x + 0.85y
1.15x + 4.15y = 5
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Comment: Need to know more about x and y to solve.
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Cheers,
Stan H.
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Probability-and-statistics/368222: How do you solve:
Powerball is played where for $1 you choose 5 out of 59 balls and you choose one powerball out of 39 balls. Show the nCr notation and your result.
a) How many ways to hit all 5 and the powerball?
Thank you!
1 solutions
Answer 262383 by stanbon(57290) on 2010-11-08 22:13:43 (Show Source):
You can put this solution on YOUR website!How do you solve:
Powerball is played where for $1 you choose 5 out of 59 balls
---
# of sets of 5 balls: 59C5 = 5,006,386
# of winning sets: 1
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and you choose one powerball out of 39 balls.
# of winning balls: 1
Show the nCr notation and your result.
a) How many ways to hit all 5 and the powerball?
1 way out of 39*5,006,386 = 195,249,054
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Save your money and you will be a winner every time.
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Cheers,
Stan H.
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